The toilet flushing device of the prior art permits a full tank of water to be emptied out in one flush for cleaning the toilet bowl even at such time when there is only a small amount of human waste in the toilet bowl. In other words, the toilet flushing device of the prior art is of a little help to the water conservation. As a result, a new toilet was developed and introduced. Such a new toilet is provided with a water tank having two water outlets located at different levels so as to permit a less than full tank of water to be emptied out. However, such a new toilet as described above is limited in that it is rather complicated in construction, and that it is not compatible with the conventional toilet.